Problem: Solve for $x$ and $y$ using elimination. ${2x+y = 14}$ ${3x+y = 19}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${2x+y = 14}$ $-3x-y = -19$ Add the top and bottom equations together. $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {2x+y = 14}\thinspace$ to find $y$ ${2}{(5)}{ + y = 14}$ $10+y = 14$ $10{-10} + y = 14{-10}$ ${y = 4}$ You can also plug ${x = 5}$ into $\thinspace {3x+y = 19}\thinspace$ and get the same answer for $y$ : ${3}{(5)}{ + y = 19}$ ${y = 4}$